A and B are two given matrices such that the order of A is 3 × 4 , if A' B and BA' are both defined then
Step-by-Step Solution
Key Concept: If A is 3x4, then A' is 4x3. For A'B to be defined, B must be 3xn. For BA' to be defined, B must be mx4. Thus B must be 3x4. Then B' is 4x3. B'A is (4x3) * (3x4) = 4x4.
Given order of A is 3 \times 4, so order of A' is 4 \times 3. For A'B to be defined, B must be of order 3 \times n. For BA' to be defined, B must be of order m \times 4. Comparing these, B must be of order 3 \times 4. Then B' is of order 4 \times 3. Thus, B'A is (4 \times 3) \times (3 \times 4) = 4 \times 4.
Correct Answer: 2